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Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 4 of 7: Beginning to explore volume as it compares to area [video]. Retrieved from https://doi.org/doi:10.7282/T31V5CW4

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 4 of 7: Beginning to explore volume as it compares to area
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-07
Persistent URLhttps://doi.org/doi:10.7282/T31V5CW4
DescriptionIn the fourth clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie refers to the Base-10 squared materials to explain the difference between area and volume to the researcher, Carolyn Maher. They extend an earlier problem modeling the square of (a+b) by considering various numbers, a and b, for which the sum of the two numbers is 10. Stephanie provides an argument for why the volume of the cube with a side of 10 units is 1000 cubic units.
The problem as presented to Stephanie:
How could you convince someone that the volume of the large cube is 1000 cubic unit?
Math ToolBase ten blocks
Math StrandAlgebra
Math ProblemConstruct volume model
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Substituting numbers for variables, Considering a simpler problem, Constructing a physical model
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student view
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Date Captured1996-02-07
Local IdentifierA64A65-ALG-BIEX-CLIP004
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 4 of 7: Beginning to explore volume as it compares to area.
   Date: 2011
   Author: Aboelnaga, Eman Y. (Eman Yousry) (Rutgers, the State University of New Jersey)

   Name: A case study : the development of Stephanie's algebraic reasoning
   Reference: http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Source
   Title: A64, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (student view), Grade 8, February 7, 1996, raw footage.
   Identifier: A64-19960207-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A65, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (work view), Grade 8, February 7, 1996, raw footage.
   Identifier: A65-19960207-KNWH-WV-INT-GR8-ALG-BIEX-RAW